This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...

In this paper, a special technique is studied by using the orthogonal Chebyshev polynomials to get approximate solutions for singular and hyper-singular integral equations of the first kind. A singular integral equation is converted to a system of algebraic equations based on using special properties of Chebyshev series. The error bounds are also stated for the regular part of approximate solut...

We are interested in the qualitative properties of positive entire solutions u ∈ C(R\{0}) of the equation (0.1) ∆u = u n+4 n−4 in R\{0} and 0 is a non-removable singularity of u(x). It is known from [Theorem 4.2, [12]] that any positive entire solution u of (0.1) is radially symmetric with respect to x = 0, i.e. u(x) = u(|x|), and equation (0.1) also admits a special positive entire solution us...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

We study persistence of periodic solutions perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular solution. The results this paper are motivated by result Holmes and Wiggins where authors considered two dimensional Hamiltonian family smooth systems depending on scalar variable which is solution singularly equation.

Optimal control of dampers has been proposed to mitigate vibration effects in mechanical systems. In many cases, systems are subject to periodic forcing and the goal is to maximize the energy dissipated by the damper. In contrast to prior work utilizing instantaneous or infinite-time−horizon optimization, this paper employs periodic optimal control to maximize the energy dissipated per cycle. F...

where a, c : Z ® R+ are T-periodic functions, f Î C(Z × (0, ∞), R) is T-periodic with respect to t and singular at u = 0. Positive periodic solutions of second-order difference equations have been studied by many authors, see [1-6]. However, in these therein, the nonlinearities are nonsingular, what would happen if the nonlinearity term is singular? It is of interest to note here that singular ...

in this paper we study the boundary layer problems in which boundary conditions are non-local. here we try to find the necessary conditions by the help of fundamental solution to the given adjoint equation. by getting help from these conditions, at first the boundary condition is changed from non-local to local. the main aim of this paper is to identify the location of the boundary layer. in ot...

We demonstrate how Sen’s singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important rôle in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action...

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...